A rectangular park has an area of 1.36×108 ft2 . The length of the park is 1.6×104 ft. Divide the area by the length to find the width of the park.(1 point)

8.5×10^2 ft.
8.5×10^3 ft.
8.5×10^5 ft.
8.5×10^4 ft.

1 answer

To find the width of the park, divide the area by the length.

Given:

  • Area = \(1.36 \times 10^8\) ft²
  • Length = \(1.6 \times 10^4\) ft

The formula for the width \(w\) is:

\[ w = \frac{\text{Area}}{\text{Length}} = \frac{1.36 \times 10^8}{1.6 \times 10^4} \]

Now, we can divide the coefficients and subtract the exponents:

  1. Divide the coefficients: \[ \frac{1.36}{1.6} = 0.85 \]

  2. Subtract the exponents: \[ 10^8 \div 10^4 = 10^{8 - 4} = 10^4 \]

Combining these results gives:

\[ w = 0.85 \times 10^4 \]

To express \(0.85\) in scientific notation: \[ 0.85 = 8.5 \times 10^{-1} \]

Thus, \[ w = 8.5 \times 10^{-1} \times 10^4 = 8.5 \times 10^{4 - 1} = 8.5 \times 10^3 \text{ ft} \]

Therefore, the width of the park is: \(\boxed{8.5 \times 10^3 \text{ ft}}\)

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